Problems
Baked Bean Cans
Stage: 1 Challenge Level: 
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Building with Solid Shapes
Stage: 1 Challenge Level:
We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?
Skeleton Shapes
Stage: 1 Challenge Level:
How many balls of modelling clay and how many straws does it take to make these skeleton shapes?
Multilink Cubes
Stage: 2 Challenge Level:
If you had 36 cubes, what different cuboids could you make?
Cuisenaire Rods
Stage: 2 Challenge Level:
What different walls can you make with different combinations of Cuisenaire rods?
Construct-o-straws
Stage: 2 Challenge Level:
Make a cube out of straws and have a go at this practical challenge.
Cereal Packets
Stage: 2 Challenge Level:
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Three Cubed
Stage: 2 Challenge Level:
Can you make a 3x3 cube with these shapes made from small cubes?
Lost in Space
Stage: 2 Challenge Level:
The image in this problem is part of a piece of equipment found in the playground of a primary school. How would you describe it to someone over the phone?
Cubes Within Cubes
Stage: 2 Challenge Level:
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Icosian Game
Stage: 3 Challenge Level:
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only– returning to the vertex you started at.
Squares
Stage: 3 Challenge Level:
Three dimensions is the theme within the main body of the magazine and although 3D LOGO does exist few appear to use it. However, within the confines of the plane a representation of space can be. . . .
All in the Mind
Stage: 3 Challenge Level:
Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .
Marbles in a Box
Stage: 3 Challenge Level:
You have 27 transparent unit cubes arranged in a 3 by 3 by 3 array. Marbles are alternately placed into the cubes by two players. How many unique winning lines of three marbles are possible?
Cubist Cuts
Stage: 3 Challenge Level:
A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?
Cutting a Cube
Stage: 3 Challenge Level:
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
Excel Investigation: Happy Numbers
Stage: 3 and 4 Challenge Level:
Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.
Excel Interactive Resource: Equivalent Fraction Bars
Stage: 3 and 4 Challenge Level:
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
Excel Technique: LOOKUP Functions
Stage: 3 and 4 Challenge Level:
Learn how to use lookup functions to create exciting interactive Excel spreadsheets.
In a Spin
Stage: 4 Challenge Level:
What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?
Plum Tree
Stage: 4 and 5 Challenge Level:
Label a graph with the numbers 1 to n, one on each vertex, one on each arc. A Totally Magic graph is both Edge Magic and Vertex Magic.
Magic Caterpillars
Stage: 4 and 5 Challenge Level:
Put numbers 1 to n on the edges and vertices of a graph so that the sum of the numbers on a vertex and on all arcs joined to that vertex is the same for all vertices.
Golden Powers
Stage: 5 Challenge Level:
You add 1 to the golden ratio to gets its square. How do you find higher powers?
Folium of Descartes
Stage: 5 Challenge Level:
Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.
